Hello George,
Welcome to hobby machining. It is a lot of fun and there is always something to learn.
Having both the mill and lathe would be a great advantage, and I feel actually necessary for projects like those you have mentioned.
I suggest buying a fairly basic lathe package which would include three and four jaw chucks and the tailstock for drilling. I would not buy the lathe milling attachment. You can mill with it, but it won't be very handy. Also, for the time being at least, I'd leave the lathe as a manual machine.
At the same time I'd buy the 2019 CR-ER mill. The ER-16 collets are a very handy. If at this point, you can proceed with CNCing the mill I'd do that and it is easy with the CNC ready mill. If you are not ready to CNC the mill, I'd add handles and run it manually to get started. The 4th axis could, in my opinion, be added later.
As you can imagine, there will be plenty of small tooling to buy. I'd buy it as needed for your projects and when it comes to taps, buy the very best from MSC, Travers, or the like. Hardware store taps will let you down by breaking off and usually in the last hole to be tapped.

A good tooling plate is nice as it helps with the work holding and protects the mill table.
I find my CNC Taig mill very useful and would hate to go back to manual only. I have a Taig lathe which I plan to CNC as I think CNC on the lathe would be nice for threading, but manual operation has worked very well for most of my lathe work. I'm not knocking the CNC lathe, but just feel I'd put my CNC money into the mill first.
Currently I use a full size manual lathe, a full size manual mill, a manual Sherline lathe, and the CNC Taig mill. I've added the small machines over the last couple years and have been amazed at how many of the small model engine parts now go to the little machines. They are very capable and seem easier to use on the small parts. The Taig lathe was a recent purchase and I bought it with CNC in mind as a future project.
So, there you have my opinions/suggestions etc all based on my personal experience and biases.

I am sure you will get good suggestions from others in the group.
Keep asking questions and join the fun.
Regards,
Chuck Kuhn